Some streaming applications like OBS allow you to specify a part of the screen to stream out. I forget if there are options to hide the cursor or not, but probably someone does it. You could also not include any dragger / mouse-sensitive behaviors and just use key triggers for hand positions (like this example 36 minutes in: Character Animator Live - Episode 1: Cesar the Zombie, Cyberman & Stick Figure - YouTube)). If you had a touch-enabled device, you could also control draggers with your fingers instead.

We realize this isn't a perfect solution and a lot of people have asked for better live support - we're currently working on some better ways to do this, so stay tuned for future releases.